The Inverse and Determinants of 2x2 and 3x3 Matrices

For those people who need instant formulas!
The general way to calculate the inverse of any square matrix, is to append a unity matrix after the matrix (i.e. [A | I]), and then do a row reduction until the matrix is of the form [I | B], and then B is the inverse of A. There is also a general formula based on matrix conjugates and the determinant.
In the following, DET is the determinant of the matrices at the left-hand side.